Question

working alone, eduardo can pick forty bushels of apples in 8 hours. micaela can pick the same amount in 14 hours. if they worked together how long would it take them? hours = minutes = seconds =

Explanation:

Step1: Calculate the rate of work for each person

Eduardo's rate of work: He can pick 40 bushels in 8 hours. So his rate $r_{E}=\frac{40}{8} = 5$ bushels per hour. Micaela can pick the same amount (40 bushels) in 14 hours. So her rate $r_{M}=\frac{40}{14}=\frac{20}{7}$ bushels per hour.

Step2: Calculate the combined rate of work

The combined rate of work $r = r_{E}+r_{M}=5+\frac{20}{7}=\frac{35 + 20}{7}=\frac{55}{7}$ bushels per hour.

Step3: Calculate the time taken when working together

Let the time taken when they work together be $t$ hours to pick 40 bushels. Since rate $\times$ time = work, we have $t=\frac{40}{\frac{55}{7}}=40\times\frac{7}{55}=\frac{56}{11}\approx5.09$ hours.

• Convert $\frac{56}{11}$ hours to minutes: $\frac{56}{11}\times60=\frac{3360}{11}\approx305.45$ minutes.
• Convert $\frac{56}{11}$ hours to seconds: $\frac{3360}{11}\times60=\frac{201600}{11}\approx18327.27$ seconds.

Answer:

Hours = $\frac{56}{11}\approx5.09$
Minutes = $\frac{3360}{11}\approx305.45$
Seconds = $\frac{201600}{11}\approx18327.27$